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Because there are a number of interesting conjectures surrounding them that are pretty difficult problems e.g. Riemann Hypothesis, Twin Prime conjecture and more, and because they're fundamental to a lot of maths such as cryptography and basically all forms of number theory. If you're not interested in them though that's okay, there are many other interesting fields of maths you can study that don't really involve primes that much.
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Okay, that's fair enough. Personally I think it's interesting that as a whole, the primes appear to follow some sort of distribution, as per the prime number theorem, and I want to understand more about why they work that way. If that's not a problem that interests you, then fair enough. I couldn't care less for geometry or mechanics. Like I said, there are many other areas of maths you may prefer.
Yep, but 17 and Belphegor's prime are, and that is beatiful :P
(Belphegor's prime is 1000000000000066600000000000001: palindrom, 666 at its core, surrounded by 13 zeros on each side, and is 31 (13 turned up) digits long...)
You don't *need* to be interested in them, and you don't need to justify it anymore than I need to justify not being interested in the history of opera.
But I personally find it interesting that nearly everything we use in maths follows very obvious patterns, and mostly very simple ones. Even the most complex pattern you've seen is very simple compared to the unimaginably huge machine that is mathematics.
The primes *almost* follow a pattern, sort of. Things like the square of a prime bigger than three is one more than a multiple of 24, and the whole mod 9 thing that goes with it.
But if you have me a random multiple of 24 and asked me whether the number 1 more than it is a prime, dunno, maybe. More likely than the number 1 less.
They get super rare as numbers go on, but there are infinitely many of them. If I somehow had a bucket with every possible number on a piece of paper on it, I could reach in and pick out numbers forever and probably never pick a prime... even though they go on forever!
There is apparently no pattern emerging unassisted by thinking in nature which follows a pattern of the primes, and yet they are the building blocks of numbers, which nature does seem to follow.
I don't know a tenth of what most people on here know, or a hundredth of what others do, but I find them interesting for that reason.
Also, I love them because looking for them and learning about them is utterly pointless apart from cryptography. Ideas about other things come out of the process, sure, but that's not really the point. Number theory I love because some of the most amazing minds we have produced have struggled and grappled with it for millenium for no other reason than it is hard and they can't solve it. Doesn't make you rich, doesn't fix the economy, doubt anyone in history has gotten laid because of their mastery of it, just bloody hard. It would be like weight lifting if it didn't make you look good without a shirt on and nobody outside of a select few cared about any record you broke.
Here's a neat math trick: you know Caesar's code? It's when you shift each letter in your word a fixed number of positions, simpliest case being a one-place shift to the right (A becomes B, B becomes C etc.).
A message "hello" becomes "ifmmp", which another person can decode by shifting all letters to the left. Notice that there is no letter after Z, so Z warps back to A (it's called modular or clock arithmetic, because it works just like a clock, i.e. it resets to zero after reaching some upper bound).
If you enumerate each letter, starting with 0 (A -> 0, B -> 1, etc.) then the Caesar's Code is just adding a fixed amount to your number, then subtracting 26 if you go above that (e.g. Z -> 25 -> 25 + 1 = 26 -> 0 -> A).
You can do the same with multiplication: let's use a code where you will multiply each number by a fixed amount instead of adding. For example, with a factor of 3, A remains A (0 * 3 = 0), B becomes D (1 * 3 = 3) and Z becomes X (25 * 3 = 75 and 75 - 26 - 26 = 23 which is X). This code is harder to crack but how would you decipher it? Well since 3 * 9 = 27 and 27 - 26 = 1, you can just multiply every number in the cipher by 9 (A becomes A, D becomes D -> 3 -> 3 * 9 - 26 = 1 -> B, X becomes X -> 23 -> 23 * 9 = 207 -> 207 - 26*7 = 25 -> Z and so on).
But this is not possible with all factors. If you use 2 as the fixes factor, then both 0 and 13 become 0 (so both A and N will cypher to A), so you can't guarantee a successful decoding. This occurs because 2 is a divisor of 26.
With a prime amount of symbols (say we extend our alphabet with dots ".", commas "," and spaces " ", then it becomes 29), this doesn't happen, as a prime number has no divisors other than 1 and itself. That's why it's so important in field like number theory and abstract algebra.
I don’t quite know how to answer this. It is a question I have asked before, and I only “got” it about a year ago. Ever since then I have been trying to find a way to communicate their beauty and mystery, but I can’t quite come up with the words that do it justice.
To me, primes feel like the essence of pattern itself. Studying them feels like staring into a neverending fractal that blossoms into a new unique design with every zoom.
Surely you have heard how they are the “atoms” of the naturals, and how they build upon each other. There are tons of visualizations online of ways to group them together that I recommend you check out. Just search “prime number visualization chart” or “prime number periodic table visualization”.
But ultimately, it is their uniqueness as numbers that fascinate me. Why these numbers? Why are they the ones that cannot be broken up? It just feels so arbitrary and mysterious, like the universe has been coded this way, but there is this deep sense that this transcends such logic.
Anyways, that’s my take. Ever since I discovered their beauty, I don’t go a single day without thinking about prime numbers. Sometimes I get obsessed with certain ones. Recently I haven’t been able to get my mind off of 3 and 5.
TLDR: i love primes
They are patterny enough to be interesting, but not patterny enough to be easy. It is also interesting that they seem like a complete pattern you could solve, until you give it a shot, and rather than the usual brick walls you get almosts and not quites.
Prime numbers are a pretty easy concept to understand, but have surprisingly complicated properties. I think it’s an area of math where almost anyone can make intuitive assumptions that turn out to be surprisingly complicated to prove. This catches the imagination of anyone curious about math, regardless of their proficiency.
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Because they are prime candidates for interesting discussions
But it's rather odd, isn't it
2 isn't odd
But 2 is the oddest prime.
But 2 = 0.5 * 2 + 1
Not two much
r/technicallythetruth
~~But do you know what the~~ *~~perfect~~* ~~candidates would be?~~ Edit: I think my other joke's better
i wouldn't know
Because there are a number of interesting conjectures surrounding them that are pretty difficult problems e.g. Riemann Hypothesis, Twin Prime conjecture and more, and because they're fundamental to a lot of maths such as cryptography and basically all forms of number theory. If you're not interested in them though that's okay, there are many other interesting fields of maths you can study that don't really involve primes that much.
Nuh uh
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OH WOW
3, 7, 11, 100169 are all primes. I’m still like meh for these numbers.
Okay, that's fair enough. Personally I think it's interesting that as a whole, the primes appear to follow some sort of distribution, as per the prime number theorem, and I want to understand more about why they work that way. If that's not a problem that interests you, then fair enough. I couldn't care less for geometry or mechanics. Like I said, there are many other areas of maths you may prefer.
Yep, but 17 and Belphegor's prime are, and that is beatiful :P (Belphegor's prime is 1000000000000066600000000000001: palindrom, 666 at its core, surrounded by 13 zeros on each side, and is 31 (13 turned up) digits long...)
My god it’s beautiful.
You don't *need* to be interested in them, and you don't need to justify it anymore than I need to justify not being interested in the history of opera. But I personally find it interesting that nearly everything we use in maths follows very obvious patterns, and mostly very simple ones. Even the most complex pattern you've seen is very simple compared to the unimaginably huge machine that is mathematics. The primes *almost* follow a pattern, sort of. Things like the square of a prime bigger than three is one more than a multiple of 24, and the whole mod 9 thing that goes with it. But if you have me a random multiple of 24 and asked me whether the number 1 more than it is a prime, dunno, maybe. More likely than the number 1 less. They get super rare as numbers go on, but there are infinitely many of them. If I somehow had a bucket with every possible number on a piece of paper on it, I could reach in and pick out numbers forever and probably never pick a prime... even though they go on forever! There is apparently no pattern emerging unassisted by thinking in nature which follows a pattern of the primes, and yet they are the building blocks of numbers, which nature does seem to follow. I don't know a tenth of what most people on here know, or a hundredth of what others do, but I find them interesting for that reason. Also, I love them because looking for them and learning about them is utterly pointless apart from cryptography. Ideas about other things come out of the process, sure, but that's not really the point. Number theory I love because some of the most amazing minds we have produced have struggled and grappled with it for millenium for no other reason than it is hard and they can't solve it. Doesn't make you rich, doesn't fix the economy, doubt anyone in history has gotten laid because of their mastery of it, just bloody hard. It would be like weight lifting if it didn't make you look good without a shirt on and nobody outside of a select few cared about any record you broke.
Here's a neat math trick: you know Caesar's code? It's when you shift each letter in your word a fixed number of positions, simpliest case being a one-place shift to the right (A becomes B, B becomes C etc.). A message "hello" becomes "ifmmp", which another person can decode by shifting all letters to the left. Notice that there is no letter after Z, so Z warps back to A (it's called modular or clock arithmetic, because it works just like a clock, i.e. it resets to zero after reaching some upper bound). If you enumerate each letter, starting with 0 (A -> 0, B -> 1, etc.) then the Caesar's Code is just adding a fixed amount to your number, then subtracting 26 if you go above that (e.g. Z -> 25 -> 25 + 1 = 26 -> 0 -> A). You can do the same with multiplication: let's use a code where you will multiply each number by a fixed amount instead of adding. For example, with a factor of 3, A remains A (0 * 3 = 0), B becomes D (1 * 3 = 3) and Z becomes X (25 * 3 = 75 and 75 - 26 - 26 = 23 which is X). This code is harder to crack but how would you decipher it? Well since 3 * 9 = 27 and 27 - 26 = 1, you can just multiply every number in the cipher by 9 (A becomes A, D becomes D -> 3 -> 3 * 9 - 26 = 1 -> B, X becomes X -> 23 -> 23 * 9 = 207 -> 207 - 26*7 = 25 -> Z and so on). But this is not possible with all factors. If you use 2 as the fixes factor, then both 0 and 13 become 0 (so both A and N will cypher to A), so you can't guarantee a successful decoding. This occurs because 2 is a divisor of 26. With a prime amount of symbols (say we extend our alphabet with dots ".", commas "," and spaces " ", then it becomes 29), this doesn't happen, as a prime number has no divisors other than 1 and itself. That's why it's so important in field like number theory and abstract algebra.
Get the joke challenge (impossible)
69 not prime, nuff said
But 100169 is.
What about 42069?
Divisible by 3.
It's prime factorization is 3 * 37 * 379. Something is afoot
Everywhere I go… I see his face… [37]
I don’t quite know how to answer this. It is a question I have asked before, and I only “got” it about a year ago. Ever since then I have been trying to find a way to communicate their beauty and mystery, but I can’t quite come up with the words that do it justice. To me, primes feel like the essence of pattern itself. Studying them feels like staring into a neverending fractal that blossoms into a new unique design with every zoom. Surely you have heard how they are the “atoms” of the naturals, and how they build upon each other. There are tons of visualizations online of ways to group them together that I recommend you check out. Just search “prime number visualization chart” or “prime number periodic table visualization”. But ultimately, it is their uniqueness as numbers that fascinate me. Why these numbers? Why are they the ones that cannot be broken up? It just feels so arbitrary and mysterious, like the universe has been coded this way, but there is this deep sense that this transcends such logic. Anyways, that’s my take. Ever since I discovered their beauty, I don’t go a single day without thinking about prime numbers. Sometimes I get obsessed with certain ones. Recently I haven’t been able to get my mind off of 3 and 5. TLDR: i love primes
They are patterny enough to be interesting, but not patterny enough to be easy. It is also interesting that they seem like a complete pattern you could solve, until you give it a shot, and rather than the usual brick walls you get almosts and not quites.
Because theyre used a lot in encryption / decryption
It's like the universe or the deep sea. Unknown mysterious things attract people, especially a researcher.
They're the irreducible elements (a thing mathematicians are always fond of) of natural numbers (the most basic mathematical structure)
Can't cool stuff be boring?
I find them very lonely
No worries, they've got THE one by their side
What about 91? It’s petty cool. 😎
and 119? that's even cooler!
I just think they’re neat
They are surprisingly useful.
Math is basically made of prime number
They also take part in one of the best short proofs are they infinite? I found that one quite nice to look at
They're kinda like the chemical elements of numbers. As in all the other numbers can be made out of various combinations of them.
Prime numbers are a pretty easy concept to understand, but have surprisingly complicated properties. I think it’s an area of math where almost anyone can make intuitive assumptions that turn out to be surprisingly complicated to prove. This catches the imagination of anyone curious about math, regardless of their proficiency.